The whole of the Lakes needs to up its game for buses, possibly even having a congestion charge. More obscure mountain walks would still require car usage but those just going to see the sights and have the odd low level walk should easily be catered for with buses.
The Lakes bus network is surprisingly good and really well promoted (if a little pricey at times) - give it a go - you will be surprised at just how good it is, and it certainly does cater for what you suggest (including, by way of the infrequent but still usefully timed Langdale Rambler, some "obscure mountain walks" though obviously not all of them and there are sizeable gaps). There are large gaps in coverage (particularly west of Windermere) but it is really not bad and mostly commercial, I believe. Also while it's not promoted it has through ticketing across connections (I only found out when a driver offered it to me having asked where I was planning to end up!)
Route map if you're interested:
https://tiscon-maps-stagecoachbus.s...umbria/The Lakes by Bus - Map Winter 0919.pdf
It's North Wales that needs its game upping, that really is very poor for an area that is very easy to serve because there are very few roads to need to run the buses down!
The one thing I think that really lets it down is the lack of decent bus stations, rather than building this railway I'd build some staffed (in summer), full-service bus stations in Ambleside (stick it on the car park behind the present stops, there's plenty of room), possibly Grasmere (again, there's a decent sized car park it could be plonked on part of, or the field next to it), Keswick and Windermere (could be done alongside the full redevelopment of the station perhaps rather than the present slightly poshed up tin shack?), and possibly a few others.
As for congestion on the A66, I've never seen it congested, but if it is just plonk some bus lanes down, it's dualled for most of its length.
TBH, building this railway now would make about as much sense as building the Conwy Valley now (though I'll admit it probably wouldn't wash away *quite* as often). As others have said I wouldn't close it if it was open, but opening a new one is a rather different case.